Robert Bosch: This summer, I finally had the time to put together a
page on my "TSP Art". It has samples of my recent pieces, a
link to a second page describing how I do what I do, and links to related
pages by Craig Kaplan and Mo. [The below is a simple loop, not a knot.]

Erich Friedman: I've made a page of Polyomino
Addition Problems. The first two are surprising! They might make good puzzles for your readers.

Sudoku Variations

A large variety of new sudoku variations is on display at hexapuzzle.com.

New
Hanayama Puzzles

Various new
metal puzzles have been minted by Hanayama, and are available at Puzzle
Master. All of them are exquisitely made, and feature only 2 to 4 pieces.
Some of the newer puzzles are Oskar's Cuby puzzle, and Serhiy's Coaster puzzle.

Survo Puzzles

Seppo Mustonen: During the past 45 years I have made statistical software,
one of them being the SURVO MM (Survo) package, which is a general environment
for statistical computing and related areas. As an application of some special
computational features (especially those related to combinatorics) of Survo I
got an idea of cross sum puzzles having something of the flavour of Kakuro but
with unique and mathematically challenging features of their own. I call them
Survo cross sum puzzles or Survo
puzzles (link to PDF). As an example, arrange the numbers 1 to 12 in the
grid below so that the rows and columns sum to the given numbers (problem 10
on page 24).

21

10

18

29

24

15

39

Poincare Conjecture Proved

Back in 2003, Perelman proved the Poincare conjecture. After several years
of study, his proof has been accepted. An excellent report on
the full story is given in The New Yorker story, Manifold
Destiny. Another Fields medal winner is Terence
Tao.

Clickmazes Update

There are new logical mazes available at Andrea Gilbert's clickmazes.com.
Oskar: When writing the challenge generator for the Active Maze, I discovered
that I could not use a genetic algortithm, as even changinging the color of only
one square would change the entire maze. I wonder whether there would be any
intelligent approach to such generator, other than brute-force search.

The Davis Megamaze (in
Sterling, Mass.) is a huge cornfield maze designed by Adrian
Fisher. A feature of the maze, in addition to the many bridges, is a series
of gates which allow for 24 different mazes. The honor system prevents a person
from passing through various gates. Oskar sent
a photo. Aerial
shot.

Material added 20 August 06

Snakes on a Plane

I saw the movie with a rowdy crowd, and had a great time. More importantly,
I did a survey of some of the snake-related 2-dimensional puzzles I knew about
for my latest maa.org column, Snakes
on a Plane. An excellent snake-touching puzzle was posted on newsgroup
rec.puzzles.
Next, Serhiy
Grabarchuk's snakes will be the subject of the next Al
Zimmermann Programming Contest. Win $500 by putting big snakes in planar
areas.

Writhings on a Cube

One puzzle I wasn't able to solve involved edge crossing. In a thrackle,
each edge crosses all non-neighboring edges. John Conway offers $1000 for a
thrackle with more edges than vertices. I tried to wrap my head around the
problem. In a planar
graph,
none of the edges cross each other. Each edge crosses 0 others, so let me call
that writhing-0. What graphs are writhing-1? That is, what
graphs have the property that each edge crosses exactly one other non-neighboring
(a neighboring edge is one that shares a vertex) edge? Edges can't cross
themselves, either. One example of writhing-1 graphs is a planar
graph and its dual. Is the cube graph (the edges of a cube) writhing-2?
I spent awhile trying to bend the edges in various ways, and the best solution
I found cheated (below). Three of the crossings
involve neighboring edges. Erich Friedman found a writhing-2 drawing of the
cube with no cheating. Can you match him?
Answer. What other simple graphs
are writhing-1 or writhing-2?

Waves on a Torus

Apple has a nice write-up on my colleague Michael
Trott. Illustrated is what happens when you drop a pebble into a torus
of water.

The American Institute of Mathematics is in the planning stages for Morgan
Hill, CA.
A video tour is
available - the architecture is amazing. The courtyard is very similar to the Alhambra,
a famous site for tiling designs. Escher pretty much started there, copying the tilings
into his sketchbook.

Bob Hearn: I've decided to make the current Subway Shuffle prototype publicly
available, via www.subwayshuffle.com.
As before, the program requires OS X 10.3. Your readers might be interested in
these puzzles. The sliding-coin puzzles you posted earlier are included as special
cases of the subway puzzles. From the
site: Subway Shuffle is a collection of
puzzles set in a subway system. You have boarded a car on the Red Line, and your
task is to reach your destination. The problem is, there are other subway cars
in your way! Each subway car can move only on its own color line: the red cars
on the Red Line, the blue cars on the Blue Line, etc. Can you shuffle the cars
from station to station, eventually moving your own car to your exit station?
Oh, and by the way, I've finished my Ph.D. thesis, "Games,
Puzzles, and Computation".

Giant Jukebox Maze

M. Oskar van Deventer: Recently, the Museum
of Technology Delft commissioned Peter Knoppers and me to build a large
sample of the Jukebox puzzle. Because of the ball bearings in the switches,
this big 300x600 mm version runs as smoothly as the electronic
clickmazes version. The two photos show the Jukebox puzzle, a big canvas
with explanatory text and Liesbeth van Hees, who is responsible for the math
collection of the museum. Another
picture.

Careful out in there. Handbook
of Mathematical Functions author Milton
Abramowitz mowed his lawn in 1958, passed out in the heat, and died. That left
Irene Stegun in charge of the project. Highlights of the ensuing story are
at the bit-player blog,
and in “Irene Stegun, the Handbook of Mathematical Functions, and
the Lingering Influence of the New Deal,” by David Alan Grier, The
American Mathematical Monthly, Vol. 113, No. 7, August-September 2006,
pp. 585-597. NIST is working on a replacement.

Eric Shamblen: I thought you might like to know
about some recent additions to the Puzzle Monster website. In Buried
Treasure,
your goal is to find the locations of 9 treasure chests on a 9x9 grid. Your
only clues are the positions of skulls on the grid, placed so that 1 chest
is within 3 squares in a direct line and another chest is at least 4 squares
away in a direct line. The
Transfigurator is a simple visual logic puzzle.
Shown six transfigurations from one shape to another, deduce what the seventh
shape will become. Both of the above links are updated daily with new challenges.

Cafe Wall Illusion in Melbourne Building

Chris Lusby Taylor: Thought you might like this picture of a building I saw
in Melbourne last week. A very simple but a very effective cafe
wall illusion.
I'm afraid I know nothing of it. I took this snap from a taxi to the airport.

Rotational V Oddity

George Sicherman: I finally made some progress with V pentomino oddities. Ironically,
I had to find a quadrirotary before I found a birotary!

Gathering for Gardner Wiki

Thane Plambeck: I just finished
a little project for Tom Rodgers and AK Peters, Ltd. to put the entire book
The Mathemagician and Pied Puzzler online,
as separate PDF files, one per article (or one big one, if you have the patience
to download it).

Will Shortz has been a friend of mine for 29 years now, so
I should mention his movie Wordplay.
Almost all of these people are members of the National Puzzlers League, which
Will (Or WILLz, for WILL short Z) inducted me into 28 years ago. I know all these
people -- many of them are contributors here. Somehow, a film about my
friends rated a 95% on the Tomatometer, making it the best reviewed movie of
the year.

2006 Nob Yoshigahara Puzzle Design Competiton

Photos of the puzzles in the 2006
Puzzle Design competition are now available.
Lots of intriguing puzzles were created. One from a previous competition, which
you can buy, is Sam Cornwell's Lost
Luggage puzzle.

Heilbronn Configurations

The best records for Heilbronn configurations were greatly extended by David
Cantrell. Erich Friedman has posted the best known solutions for circles, squares,
and triangles.

Water Pouring Puzzle:

Cihan Altay: You have two containers with 8-liter and 9-liter capacities.
Some water is in each, at given temperatures and volumes. Get some
water at a temperature as close to 35 degrees as possible. No guesswork; you
must be able to know what the resulting temperature exactly is. Answers
and Solvers.

Anyone who read Martin Gardner's columns will be familiar with the Fairy Chess
Review. George Jelliss has posted a full review at his new site, mayhematics.com.

Attacking Chess Pieces

Erich Friedman: I finally
figured out how to attack every square of an nxn
chess board exactly once or exactly twice for n=5, 6, and 7. But i can't seem
to figure out how to attack each square exactly 3 (or 4 or more) times for those
values of n. Perhaps your wise readers can do it.

Bob Abbott writes: Here is the ultimate sudoku variation—Binary
Sudoku:
And
(spoiler alert! spoiler alert!) here is the solution:
There are 10 possible boards, each more exciting than the other (of course,
that's the binary number 10). [Ed - Be sure to check out the mazes on his
Logic Mazes site.]

WolframTones is now a free service.
If you have a Cellular Phone, put cellular automata music on it.

Material added 25 June 06

Entropy

Eric Solomon: you might be interested in the game program 'Entropy' at ericsolomon.co.uk/en/entropy.html.
I produced
the board game around 25 years ago, but the program is new. One player tries
to produce symmetrical patterns while the other tries to prevent them.

Alphabet of Very Obscure Animals

I enjoyed a recent
poster by artist Roz Gibson. It's an entire alphabet of some of the most
obscure birds and mammals in the world. Can you identify all of them?

Chess Competition

Itamar Faybish: I am organizing for the first time a chess composition tournament,
The Longest
Series Help-Stalemate Tournament. This tournament is the third in
the series of finding the longest series help-stalemate with a specific final
position. The first two were held by Jean-Marie Choreïn (with the assistance
of Michel Caillaud for the first one). Some sample puzzles are at my Chess
Puzzles page.

Golly 1.0

Golly 1.0, an excellent cellular
automaton explorer, has just been released. Now there's Python scripting support
if you have Python installed. A large pattern collection with incredible pieces
of Life engineering included. A star attractions is a set of "metacell" Hashing-Example
patterns by Brice Due, discovered of days ago. Like David Bell's original "unitcell",
these are large square Conway's-Life patterns that, when placed in a large grid,
can emulate any outer totalistic CA rule. Unlike previous unitcells, these metacells
change state in a way that's quite visible even at huge zoom levels, and they're
optimized in size and timing so that Golly can run them impossibly quickly.

World Puzzle Championship US Qualifier

The results are in for the WPC qualifier.
Coming in at #1 and #2, one point away from each other, were Thomas Snyder and
Wei-Hwa Huang. A full summary is
available. Many frequent contributors here contributed the puzzles used int he
competition.

Andrew McFarland: Hi, just bringing to your attention some good
laser puzzles.
Some of the levels do not use all the mirrors, and sometimes, when all the pieces
are used, one or two pieces may not be used to their fullest potential. Good
puzzles nonetheless.. and knowing a little graph theory can help.

Cesium Explosion, Soccer Balls, and Statistics

The progression of water-alkali reactions, lithium - sodium - potassium - rubidium
- cesium, is well known, but there hasn't been a good video on the web I could
point at. The folks at Brainiac show how
to blow
up a bathtub with Cesium. Also on Google Video, Michael Trott uses a soccer
ball animation to visualize a mathematical construction for a triple-cover
of the Riemann sphere. If that's not enough, you can also look at the Statistics
Rap. [UPDATE - The
cesium explosion was FAKED, by placing a bomb
in the bathtub. I asked Theo Gray for his reaction: I KNEW IT!!! Didn't I tell
you they must have faked that! And they most definitely did *not* tell viewers
that it was faked: I watched the entire show, not just the clip that has been
circulating, and I was particularly listening for any details about exactly what
they did to make such a spectacular explosion. I definitely would have remembered
if they said "oh,
by the way, we put a BOMB in there along with the cesium"!]

Non-Attacking Queens Game

In the May 2006 issue of College Mathematics Journal, page 223, Hassan
Noon and Glen Van Brummelen looked at a game where players take turns placing
non-attacking queens on a chessboard. The first to play a queen that attacks
another, loses. For odd-sized boards, the first player has an easy win (play
in the center and mirror). On the 5x5 and 7x7, there is also, ignoring
rotations and reflections, a single move off the center that also wins. Can you
find them? For even-sized boards up to 8x8, the first player wins, with a single
winning move on the 8x8. On the 10x10 board, though, the second player wins.
Nothing is known for higher order boards.

Inkscape .44 and SVG contests

The latest version of Inkscape is out.
I feel that vector drawing skills are incredibly important now, which is one
reason I am holding a Vector
Drawing contest. As of today, one person has entered.
That will certainly make judging easy. Another contest is to make an SVG
logo.

The SVG Pentominous Puzzle

Alexandre Owen Muniz: Here are a couple of puzzles
(SVG) of a new type I came
up with. The smaller one is pretty easy, but it makes a nice example. The Rules:
Divide the squares of the puzzle (white squares only) into a number of pieces.
Each piece must contain at least one letter. It must be possible to place each
pentomino in exactly one position such that: 1. it is entirely within one of
the pieces, and 2. it contains the letter corresponding to itself. (You can unhide
the solution layer to view the solutions.) [Ed - Beautiful! I love having layers
available to me. In Inkscape, the Layers bar is on the bottom left.]

Would you buy a bubble from this man?

The latest Wolfram Research party had a carnival theme. My own event challenged
people to describe the soap film that would appear within various polyhedra skeletons.
I used the Zome system for
the polyhedra.

Shaw Prize for Mathematics

The 2006 $1-Million dollar Shaw Prizes,
considered the Nobels of the East, have been announced for 2006. David Mumford
of Brown University made advances in pattern theory and vision research. Wu Wentsun
of the Chinese Academy of Sciences advance the field of mathematics mechanization.
Both will be honored at a ceremony in Hong Kong on September 12.

According to Harvard mathematics professor Shing-Tung Yau,
winner of the Fields
Prize in 1982, the global collaborative work for a proof of the Poincaré Conjecture is
now complete.

In 1982, Columbia University mathematician Richard Hamilton
showed that a compact manifold with positive Ricci curvature evolves toward
a state of constant curvature. His paper gave an initial framework to prove Thurston’s
geometrization conjecture, of which the celebrated Poincaré conjecture
is a special case. (Willam P. Thurston won a 1982 Fields medal for this work.)

In
2003, Russian mathematician Dr. Grigori Perelman gave a series of public lectures
at the Massachusetts Institute of Technology. These lectures, entitled "Ricci
Flow and Geometrization of Three-Manifolds," were presented as part of the
Simons Lecture Series at the MIT Department of Mathematics on April 7, 9, and
11 of that year. These widely acclaimed lectures made spectacular advances
to the work of Hamilton, and led to MathWorld article Poincaré Conjecture
Proved -- This Time for Real. The Perelman lectures gave a roughly 70 page
guideline for a final proof.

In 2006, the 300-page paper "The Hamilton-Perelman Thoery of Ricci
Flow-The Poincare and Geometization Conjecture," was was published in the June
issue of Asian Journal of Mathematics. Zhu Xiping of
Zhongshan University and Cao Huaidong of Lehigh University
co-authored the paper, which finalized the earlier work of Thurston, Hamilton,
and Perelmen.

Zhu and Cao spent two years writing their paper, under guidance
from Shing-Tung Yau. Once completed, they then went to Harvard for half a year.
Each week, they spent three hours explaining and defending their
work to a team of Harvard mathematicians. After this long series of lectures
and reviews, the 31 members on the editorial board of Asian
Journal of Mathematics reached a unanimous consensus to publish the
paper.

Prime Generating Polynomial Records

The latest Al Zimmermann Programming contest shattered
all existing records in the field of Prime Generating Polynomials. For
example, one polynomial that generates 49 primes is x^4 - 97*x^3 + 3294*x^2
- 45458*x + 213589, first found by Mark Beyleveld and later by 5 other participants.
Six people found this record-setting polynomial within weeks of each other!
When I suggested the contest, I had an idea that there might be some easy records
out there, but this is better than anything I expected.

Michael Trott: A few weeks ago, Dana Mackenzie contacted me and asked if
I could create some graphics for an article in American Scientist "The
Topology and Combinatorics of Soccer Balls", by Dieter Kotschick, that
Dana was editing at this time. Using various code pieces from the
GuideBooks about tori, polyhedra, knots,
Riemann surfaces, and the Weierstrass elliptic function, I created the graphics
shown in the article. As steps towards the graphics, the following
animations were created. [Ed: I didn't know a soccer ball could be deformed
like that.]

The 15 Puzzle

Many people, including me, believed that Sam Loyd created the 15 puzzle. Sam
was responsible for many frauds, but I assumed that wasn't one of them. Jerry
Slocum's latest book, The 15 Puzzle,
sets the record straight.

Martin
Gardner:
"Jerry Slocum and Dic Sonneveld have written an amazing tour de force. It covers
in fantastic detail the history of the greatest mechanical puzzle craze ever
to sweep not only the United States but also England and Europe. The Rubik’s
Cube mania was modest in comparison. Did Sam Loyd, America’s greatest puzzle
maker, invent the notorious 14-15 sliding block puzzle? He claimed he did but
the claim was a total lie. Loyd had nothing whatsoever to do with either the
puzzle or its popularity. The research done by the two authors is awesome. It
is a book hard to put down."

Jerry's book documenting Sam Loyd's skulduggery
is excellent. Ironically, on April 1 Jerry won the AGPC
Sam Loyd Award, one of puzzledom's highest
honors.

Wei-Hwa's Puzzle Challenges

The DaVinci Code puzzle challenge was very popular, and has now morphed into
Wei-Hwa's Puzzle Challenges. If you have a customized Google page, you can visit googlepuzzles and
click the Add to Google button. His latest puzzle is based on Erich Friedman's Distance
puzzles.

18 pages of puzzles

Dave Millar has posted 18 pages of puzzles at
The Griddle (.net). Probably the best collection of 4x4 themed puzzles with stars
ever assembled.

Chessudoku Book

I've mentioned Matt's
Puzzle Corner before, when he made some chess sudoku puzzles. His book Chessudoku is
now available. Matt tells a story with before each variant, with the major
characters being the White Queen, the Black Knights, and so on. A lovely book
- a free PDF preview is available.

Iridium Slabs and the High Price of Rhodium

Back when I was helping with the Periodic
Table Table, one of the difficult elements was Rhodium.
It's the rarest of all the non-radioactive elements, on par with Iridium. Back
then, in 2003, it was $380 an ounce. Now, it's $6000 an ounce. I sure wish
I'd bought more. Writer Oliver Sacks long had a desire for a slab of Iridium,
and obtained
one. His whimsy wound up being a tremendous investment.

The latest issue of popsci had this quote from
the American Institute of physics. "We were off by 39 orders of magnitude:
in PNU 775, the RHIC (Relativistic Heavy Ion Collider) peak energy density
achieved is 15 GeV per cubic femtometer, not per cubic centimeter." 39 orders
of magnitude is the difference in volume between the sun and a grain of sand.

Mahmood Saghaei: Having in mind the sudoku game I tried to do the same with
a completed knight tour and the result was XKnight
Game. XKnight is a new game
based on knight's tour problem. It is a completed knight's tour in which as many
squares as possible have been cleared provided that the resulted incomplete board
has only one valid solution. Therefore the object of the game is to find the
missing squares (Move numbers).

Material added 04 June 06

Vector Math Poster contest

I'd like to see what sort of math diagrams people are capable of. So, I am
kicking off my first Vector Math Poster contest. Depending on the number of entries
received, the first prizes will be anywhere from $100 (if less than ten people
enter) to $500 (if more than a 100 people enter). There is one major rule --
your submission must be entirely in Vector
format. If it uses any raster material
at all, it's disqualified. Other than that, it should be a single page Math poster,
suitable for hanging up in a high school or college math room, or suitable in
a background in Numb3rs, or usable as part of a background screen or
slideshow. Preferably all 5. The poster should have have some manner of math
illustration or illustrations in it, along with a good explanation of the concept.
If you use a reference, note the reference on your poster. Final deadline is
August 1. Send
me your math posters! Both TpX and Inkscape might
be useful. The formats I
prefer are SVG (favorite), PDF, EPS, DXF, AI, EMF, SWF (in that order).

2006 Google U.S. Puzzle Championship

If you'd like to be in the competition for the next US Puzzle Champion, visit
http://wpc.puzzles.com/ before June 15.
The actual test will occur June 17. There are 5 excellent puzzles in the practice
test.

John Cartan presents a seemingly simple puzzle at his Starmaze page.
That starts his own personal exploration of the problem, which eventually leads
him to the 9-dimensional hypercube. It's a huge, well-illustrated exploration,
and one of the most fascinating studies I've seen. [Now linked at Metafilter.com]

5D Rubik's cube

For those of you needing a 5 dimensional challenge, you can try 5D
Rubik's cube.

Me, Dr. Szilassi, and a Fano plane column

Here's a photo of me (denim shirt) with a Szilassi polyhedron, next to Dr.
Szilassi (suit and tie). Here's another of just me (boy
do I look tired). The builder of the object was Hans
Schepker (who can make anything
in glass). Photo by Sándor Kabai. I
touch on this polyhedron in my lastest maa.org column on the
Fano plane. We met at G4G7.

Puzzle Classics

Serhiy Grabarchuk has posted a page of Puzzle
Classics, all with new twists.

Snakes on a Plane problems

At the moment, the top problem for
the next Al Zimmermann contest is Zigzag
Paths, based on Serhiy Grabarchuk's Matchstick
Snake problem. There are many other interesting problems also being considered.
Oddly, the other leading contest is Protein
Folding, which could also be described as
a "snakes on a plane" problem.

Snakes on a Cube

The flash game 3D
Logic challenges you to make snaky connections on the surface
of a cube.

Don't try this at home

In the United States, the teaching of science and chemistry is being heavily
sanitized. A recent Wired
article starts with the owner of United
Nuclear being
arrested by the FBI, for selling common chemicals.

Pentadecathlon.com

Dave Greene: There's an ongoing catalog of new Game of Life results and current
open problems at pentadecathlon.com.
My own most recent contribution is a Life oscillator with a period that's a 12-digit
prime number. Some randomly selected highlights (and here
are more):

Based on a recent 41-cell construction by Bill Gosper, Nick Gotts produced
a pattern with only 26 ON cells that exhibits
O(t ln t) growth.

Golly is an open source, cross-platform
Game of Life simulator currently under development by Andrew Trevorrow and Tomas
Rokicki. "Our goal is to write a world-class Life simulator, solicit ideas and
help from the planet's best Life hackers, and share some of our excitement."
[Ed: This is the best available free cellular automata program, in running with
Life32 and MCell.]

Tetromino Games

Erich Friedman's latest Math Magic concerns tetromino
games. Each player has lots of copies of a particular tetromino, and alternate
playing on a rectangle. Who wins the game? He presents several interesting
cases, and asks for larger solutions.

New Robert Abbott Maze on Cover of Games

Robert Abbott has a multi-state maze on the cover of GAMES Magazine. I just
got my copy, so it should be on newsstands now. The cover shows a network of
pipes to travel through. At each junction you must exit on a pipe at the upper
left or upper right of the junction. At various times, you turn the magazine
90° clockwise. That changes where upper left and upper right point, and it
is what makes this a multi-state maze. At each junction you are in one of four
states, depending on the current orientation of the magazine.

Sudoku Ancestors

Christian Boyer: Bonjour, Ed. Here is the English
version of the press release,
as sent by Pour La Science to English-speaking press. [The
PDF shows a problem published in France,
in 1895, which can be solved exactly as a Sudoku.]

Squiggly Sudoku

Bob Harris: Well I finally managed to get Squiggly
Sudoku together, online,
and available for purchase. It's at lulu.com.
Pretty cool to have my name on a book, but it'll be cooler if and when someone
I don't know buys a copy. Also, I have updated my N-1-hint
Sudoku existence page to reflect a discovery of something similar made in
2001, at a Russian site (link available through the link above). The site was
brought to my attention by Cihan Altay. [Ed - It's a great book. I particularly
like how his solutions come with a logic sequence, allowing gentle help if you
get stuck. Below, I give an example he sent on my name, with GREP DJ in each
row, column, and region. He sent me 36 puzzles. Bob also
made the recent Martin Gardner sudoku in Scientific
American.]

Unintentional puzzle improvement

Funny story behind my domino sudoku in Scientific
American -- the domino placements
were accidently left out in the printed puzzles. Fortunately for me, this wound
up making it a much harder and much better puzzle.

White to play, and win a piece in 516 moves.

Black's best move in the following position is Rd7+. After that, White can
force a win in 516 moves. Marc
Bourzutschky: The ending kqnkrbn contains maximal
lines with 517 moves. This was a big surprise for us and is a great tribute to
the complexity of chess. The database was generated with Yakov Konoval's program.
Generation and verification took a little over a month on a 3.8 GHZ machine.
Yakov and I had thought it so unlikely that any 7-man ending would require more
than 511 moves that we had hard-coded 511 in a number of places. ... Returning
to kqnkrbn, the 517 moves continue the trend of more than doubling of depth for
each additional piece added: krk=16, kbnk=33, knnkp=82, krnknn=243, kqnkrbn=517."

New Polyhex Oddities

Col George Sicherman: It's a full-symmetry oddity for the F pentahex. [More
at the Colonel's site.
He also found a solution for the J pentahex.]

Our Deformed Solar System

From Physics News Update 778. Having
traveled far beyond the planets in their 28.5-year journey, the two Voyager spacecraft
are providing new information on the heliosphere, the teardrop-shaped bubble
that separates the solar system from interstellar space. At this week's Joint
Assembly Meeting in Baltimore of the American Geophysical Union (AGU) and several
other geophysics-related societies, Ed Stone of Caltech reported that the heliosphere
is deformed, according to Voyager observations, with the teardrop's rounded edge
bulging at the top (the northern hemisphere of the solar system) and squashed
at the bottom (the southern hemisphere). Pictures and movies at nasa.gov.

Geomag Polyhedra

Rafael Millán: We have not talked before, but I have had many good times
reading your math games and puzzles pages, for instance your magnetic
spheres article. Not using magnetic spheres, but magnetic rods and normal
steel spheres, all Platonic, Archimedean, and Johnson solids can be built, and
also many more interesting figures. I am beginning to publish a related site
(Geomag Polyhedra). I like
most the pages related to the rhombicosidodecahedron, which is perhaps the most
productive of these objects. I use the Geomag system, which uses just one rod
length. This is a challenging restriction, but it is also a stimulating one,
which also feels very "mathematical".

2006 Tessellation Contest

Jeff Tupper: Tess lets one play with
tessellations and a few types of orbifolds (tori, bi-infinite cylinders, infinite
cones, and planes; & hopefully more in the future). We've just had our 2006
Tess contest & I invite people to come by our site in a few days to see the
winning entries. Many very good entries were sent in.